Question

a student is randomly selected from this table. what is the probability that they are a senior, given that they are a boy? students on a team boy 7 9 7 5 girl 5 5 4 2 p(senior | boy) = p(b|a) = \frac{p(a and b)}{p(a)}

Explanation:

Step1: Calculate the number of boys

Add up the number of boys in each grade: \(7 + 9+7 + 5=28\)

Step2: Find the number of senior - boy

From the table, the number of senior - boy is \(5\)

Step3: Calculate the conditional probability

Using the formula \(P(\text{Senior}|\text{Boy})=\frac{\text{Number of senior - boy}}{\text{Number of boys}}\), we substitute the values: \(P(\text{Senior}|\text{Boy})=\frac{5}{28}\)

Answer:

\(\frac{5}{28}\)